how to fix jagged vertices
Thoose jagged artifacts are happening because you're trying to push the geometry over its natural boundaries: the mesh should remain evenly spaced, manifold, without overlapping and intersecting geometry.
This can be reached with more subdivisions and an accurate building of the strokes.
3k vertices is extremely low for a sculpt, this level should be used only for defining main planes and forms, further details need lot more geometry, it's usual to go up to 100K for a mid detailed model, and more than 1 milion for a full detailed one.
Make some experiments to check which is the number of vertices your machine can handle without crashing or lagging, and make use of Dynamic Topology, which adds geometry only where you sculpt.
During learning process, I find it useful to turn on the geometry viewport overlay, to better see the effects of strokes and dynatopo.
Be aware anyway that fixing the problem with so little geometry is simply impossible.